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# Write the quadratic function f(x) = 3x^{2} - 6x + 9 in vertex form.

**Solution:**

Vertex form of a quadratic equation refers to (x - h)^{2} = 4a (y - k) form or (y - k)^{2} = 4a (x - h) form depending on whether the square is on x-term or y-term respectively.

Given quadratic function is f(x) = y = 3x^{2} - 6x + 9

In the given equation square term is for x.

∴ Equation must be reduced to (x - h)^{2} = 4a (y - k) form.

We have y = 3x^{2} - 6x + 9

⇒ y = 3 (x^{2} - 2x + 3)

⇒ y = 3 (x^{2} - 2x + 1 + 2)

⇒ y = 3 [(x - 1)^{2} + 2]

⇒ y = 3(x - 1)^{2} + 6

⇒ y - 6 = 3(x - 1)^{2}

⇒ 3(x - 1)^{2} = y - 6

The above equation is in the vertex form.

## Write the quadratic function f(x) = 3x^{2} - 6x + 9 in vertex form.

**Summary:**

The vertex form of the given quadratic function, f(x) = 3x^{2} - 6x + 9, is 3(x - 1)^{2} = y - 6.

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